Niku Määttänen and Marko Terviö ETLA and Aalto University 22 November 2018, Bank of Estonia

1. Welfare Effects of Housing Transaction Taxes:
A Quantitative Analysis with an Assignment Model
Niku M¨a¨att¨anen and Marko Tervi¨o
ETLA and Aalto University
22 November 2018, Bank of Estonia
M¨a¨att¨anen and Tervi¨o 2018-10-13 1 / 20

2. Introduction
Introduction
Economists tend to see transaction taxes (aka stamp duties) as very
inefficient taxes. They distort the matching of diff. houses with diff.
households.
However, the literature does not provide a systematic quantitative
evaluation of this distortion.
We quantify the welfare cost of transaction taxes focusing on the
distortions in the matching of houses with households.
M¨a¨att¨anen and Tervi¨o 2018-10-13 2 / 20

3. Introduction
Introduction
Economists tend to see transaction taxes (aka stamp duties) as very
inefficient taxes. They distort the matching of diff. houses with diff.
households.
However, the literature does not provide a systematic quantitative
evaluation of this distortion.
We quantify the welfare cost of transaction taxes focusing on the
distortions in the matching of houses with households.
Model question:
How to quantify the welfare effects of this distortion?
M¨a¨att¨anen and Tervi¨o 2018-10-13 2 / 20

4. Introduction
Introduction
Economists tend to see transaction taxes (aka stamp duties) as very
inefficient taxes. They distort the matching of diff. houses with diff.
households.
However, the literature does not provide a systematic quantitative
evaluation of this distortion.
We quantify the welfare cost of transaction taxes focusing on the
distortions in the matching of houses with households.
Model question:
How to quantify the welfare effects of this distortion?
Applied questions:
What is marginal and total welfare cost of transaction tax?
What does the Laffer curve look like?
Why do transaction taxes persist despite the efficient alternative?
M¨a¨att¨anen and Tervi¨o 2018-10-13 2 / 20

5. Introduction
Estimated welfare costs based on empirical studies
Berard and Trannoy (2018), Besley et al. (2014), and Slemrod et al.
(2017) find only weak or no long-run effects.
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6. Model
One-sided Assignment Model with Income Effects
M¨a¨att¨anen and Tervi¨o (JET 2014): No transaction costs
Fixed quality distribution of indivisible houses.
Exogenous initial joint distribution of income and house quality.
One-to-one matching of households and houses (before and after)
Concave utility in housing quality x and composite good y: u (x, y)
Budget constraint: wealth = spending
wealth: θ + p(˜x), income θ, initial house ˜x
spending: y + p(x), consumption y, final house x
M¨a¨att¨anen and Tervi¨o 2018-10-13 4 / 20

7. Model
One-sided Assignment Model with Income Effects
M¨a¨att¨anen and Tervi¨o (JET 2014): No transaction costs
Fixed quality distribution of indivisible houses.
Exogenous initial joint distribution of income and house quality.
One-to-one matching of households and houses (before and after)
Concave utility in housing quality x and composite good y: u (x, y)
Budget constraint: wealth = spending
wealth: θ + p(˜x), income θ, initial house ˜x
spending: y + p(x), consumption y, final house x
Prices endogenous, except lowest quality house p0.
Equilibrium: demand and supply of every house type equal, while
households maximize utility
Positive assortative matching (PAM) by household wealth and house
quality (but wealth is endogenous!)
M¨a¨att¨anen and Tervi¨o 2018-10-13 4 / 20

8. Model
Model with transaction costs
M¨a¨att¨anen and Tervi¨o (2018)
Movers pay
- proportion τ of purchase price
- fixed transaction cost ζ
Non-movers consume endowment
Household {xi , y} problem is
max
j
u xj , y + pi − pj − 1{i=j} [ζj + τpj ] .
It is not worth paying the transaction cost for small moves →
no-trade region
M¨a¨att¨anen and Tervi¨o 2018-10-13 5 / 20

9. Model
Equilibrium with transaction costs
0.0 0.2 0.4 0.6 0.8 1.0
0
1
2
3
4
i
y
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10. Calibration
Calibration
Cross-section data (Helsinki MA 2004) on household income, financial
assets, and house value
Fix the length of the (single) model period (10 years) and interest rate
Translate wealth, prices and income accordingly
Match the share of households that trade (about 1/3)
Strategy:
Assume CES-utility function at various elasticities,
set real transaction costs at 4% of (initial) house prices.
Estimate empirical average relation between non-housing
consumption and house price
Interpret it as reflecting the equilibrium of the model
→ implied distribution of x (up to a constant)
Choose initial joint distribution of income and house quality so that
resulting equilibrium is close their empirical relation and the share of
traders is realistic
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11. Calibration
House prices: data
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12. Calibration
House prices: model vs. data, deviations
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13. Calibration
House prices and consumption: model vs data
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14. Calibration
House prices: calibrated income process
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15. Results
Share of households that trade
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16. Results
Laffer curve
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17. Results
Measuring welfare effects
Replace a given transaction tax with revenue equivalent property tax
Welfare measure:
Compensating variation (CV) for the tax reform
In some cases CV would depend on x0, so we can only evaluate
- ex post welfare (households anticipate their shocks)
- ex ante only under log-utility
Impact on “always-traders” included
M¨a¨att¨anen and Tervi¨o 2018-10-13 14 / 20

18. Results
Marginal cost of public funds
0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09
τ
2
4
6
8
10
12
MC
ε
2
3
1
4
3
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19. Results
Comparison with the empirical literature
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20. Results
Welfare gain: property tax vs. tr. tax
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21. Results
Proportion of winners: property tax vs. tr. tax
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22. Results
On the difficulty of transaction tax reform
If most households anticipate their potential gains from trade in the
near/medium term...
Despite aggregate gains, many/most would be worse off ex post
Share of losers increasing in the initial transaction tax rate
Never-movers obviously worse off, they just pay more taxes.
Many marginal induced movers worse off:
small gain from trade vs discrete increase in tax burden
Increase in tax burden increasing in initial transaction tax rate
Higher real transaction cost → fewer sure winners from the reform
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23. Summary: housing transaction tax and welfare
New framework for welfare analysis in one-sided matching markets.
Focus on matching of houses and owner households within MA.
Calibration: Helsinki MA
- Average welfare cost of a small transaction tax is not large
- MCPF increases rapidly with the tax rate
- Laffer curve peaks around 10 %
Despite aggregate gains, many households would be ex post worse off
under revenue equivalent property tax
- Sticky tax! Reform may be harder the higher the transaction tax rate
M¨a¨att¨anen and Tervi¨o 2018-10-13 20 / 20

24. Extra
Spare slides
. . . if time permits
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25. Extra
Inference of house type distribution
Observe joint distribution of income y and house prices p
– Need E[y + p|p] increasing in p
x and u not observed
Assuming u, distribution of x can be inferred from cross-section:
Which distribution of x results in the empirical relation of income and
house prices as the equilibrium of the model
Use inferred x’s and u with counterfactual tax regime to generate
counterfactual allocation.
Scale of x is not defined (x0 can not be inferred)
– ask only questions where answers don’t depend on x0
M¨a¨att¨anen and Tervi¨o 2018-10-13 20 / 20

26. Extra
Alternative: Property tax
Everyone pays
- property tax at rate t of house they consume
Movers pay
- fixed transaction cost ζ
Household {xi , y} problem is
max
j
u xj , y + pi − (1 + t)pj − 1{i=j}ζj .
Smaller transaction cost → smaller no-trade region
M¨a¨att¨anen and Tervi¨o 2018-10-13 20 / 20

27. Extra
Calibration details
One model period 10 years. Transform income and all housing costs
accordingly with 5 % interest rate.
CES utility, vary assumed elasticity {2/3, 1, 4/3}.
Discretize to 100 house types.
Start with 2 % transaction tax and 4 % (other) transaction cost.
M¨a¨att¨anen and Tervi¨o 2018-10-13 20 / 20

28. Extra
Calibration details
One model period 10 years. Transform income and all housing costs
accordingly with 5 % interest rate.
CES utility, vary assumed elasticity {2/3, 1, 4/3}.
Discretize to 100 house types.
Start with 2 % transaction tax and 4 % (other) transaction cost.
Trade caused by income shocks yi = ¯yi (1 + δi )(exp(ε)/s), where ε is
distributed N(0, σε)
“Mean reversion” δk = a0 + a1k + a2k2 + a3k3
Search for ah and σε to minimize MSE between ¯yk and ˜yk, such that
share of households trading equal to 33%
M¨a¨att¨anen and Tervi¨o 2018-10-13 20 / 20

29. Extra
Average house price
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30. Extra
Sensitivity: Revenue, Volume, Prices
Tax revenue Trade share Avg. price
€/hh % €1000s
τ 0.02 0.08 0.02 0.08 0.02 0.08
Elasticity Low 198.9 408.8 32.8 17.4 238.7 229.2
High 235.8 486.8 33.5 17.4 246.4 232.6
Fixed
cost
Low 199.9 304.8 32.6 12.7 236.4 225.7
High 231.2 549.0 33.6 20.4 245.2 232.0
Interest
rate
Low 222.4 471.8 33.1 17.8 241.2 219.3
High 219.6 447.9 33.0 17.2 239.3 230.8
Calibrated 220.5 452.4 33.4 17.5 244.9 232.7
M¨a¨att¨anen and Tervi¨o 2018-10-13 20 / 20

31. Extra
Sensitivity: Welfare
Welfare gain Winners E Welfare gain E Winners
€/hh % €/hh %
τ 0.02 0.08 0.02 0.08 0.02 0.08 0.02 0.08
Elasticity Low 25.7 222.6 38.5 34.8
High 28.6 259.0 39.1 35.0
Fixed
cost
Low 41.4 294.5 41.8 38.8 30.8 257.5 96 100
High 20.4 205.4 37.6 33.7 -4.5 119.9 33 69
Interest
rate
Low 25.1 219.1 38.3 34.2 8.1 154.8 18 58
High 28.2 251.2 38.7 35.1 9.8 191.9 62 100
Calibrated 27.7 244.6 39.0 35.2 9.3 182.1 57 100
M¨a¨att¨anen and Tervi¨o 2018-10-13 20 / 20

32. Extra
Distributional effects of tax reform: low tax, median i
20 000 40 000 60 000 80 000 100 000
y
-500
0
500
1000
1500
2000
2500
3000
M(y|h)
τ = 0.02
M¨a¨att¨anen and Tervi¨o 2018-10-13 20 / 20

33. Extra
Distributional effects of tax reform: high tax, median i
20 000 40 000 60 000 80 000 100 000
y
-500
0
500
1000
1500
2000
2500
3000
M(y|h)
τ = 0.08
M¨a¨att¨anen and Tervi¨o 2018-10-13 20 / 20